Answer: Not provided

The calculation shows the risk-neutral probability of an up move in a binomial tree model. Given: - r = 12% annual interest rate - Δt = 3/12 = 0.25 years - u = 1.2 (up factor) - d = 0.8 (down factor) The formula for risk-neutral probability is: $$ P_{\text{up}} = \frac{e^{r\Delta t} - d}{u - d} $$ Substituting the values: $$ P_{\text{up}} = \frac{e^{0.12 \times 0.25} - 0.8}{1.2 - 0.8} = \frac{e^{0.03} - 0.8}{0.4} = \frac{1.03045 - 0.8}{0.4} = \frac{0.23045}{0.4} = 0.576125 \approx 57.61\% $$

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